Socially-maximal Nash equilibrium distributions in large distributional games

Abstract We formulate the notion of a socially-maximal Nash equilibrium distribution in a large distributionalized game with traits, and show that a socially-maximal Nash equilibrium distribution exists. We also show that no-where equivalence condition is not only sufficient but also necessary to the existence of a socially-maximal Nash equilibrium in a class of large individualized games with traits.